[en] Unsteady hydromagnetic thermal boundary layer flow of an electrically conducting, viscous, incompressible fluid near a harmonically oscillating limiting surface (e.g. in stellar atmospheres) is considered when the viscous dissipation and the Joule heating terms are retained in the energy equation. Exact solution of the problem, with the aid of the Laplace transform technique, is obtained when the magnetic Prandtl number is unity. For the purpose of application and discussion of the results, the variations of the temperature and the rate of heat transfer (expressed in the form of the Nusselt number) are presented for different sets of values of the magnetic parameter for the case of two particular fluids-air and water-when the limiting surface is under the condition of either cooling or heating. (Auth.)